How do you make it in a man’s world? If there’s one person who should know, it’s Christine Lagarde, the head of the International Monetary Fund. Before leading one of the world’s most powerful financial international organizations, she was the first female finance minister of a G8 economy.

So when she took to the stage at the Women in the World Summit in New York, one of the first questions put to her was whether she thought more women could follow in her footsteps and make it to the top.

Niall Ferguson, the Harvard professor who was interviewing Lagarde, didn’t sound too hopeful. “It seems as if the world is going the wrong way. There’s a kind of nasty, macho streak in politics,” he said referring to the US, but adding that it was a wider trend. “You said recently in an interview that for a woman to get to the top, she needed ‘skin as thick as an old crocodile’. I don’t find that very encouraging. Can you give the women in this audience some hope that you can get to the top without crocodile skin?”

Her answer? If women want to succeed, they need to be thick-skinned – aggressively determined and impervious to criticism – at least to begin with: “I regret to say that the crocodile skin is unfortunately a sine qua non for a period of time.” But once a woman is established, “she can take off the crocodile skin and become a normal human being, without having to shield against horrible attacks and below the belt punches.”

It’s in line with the thinking of people like Sheryl Sandberg, Facebook’s COO and one of the most influential women in business. In 2013, her best-selling book called on women to “lean in” at work. Others have questioned the idea that women should have to act like men to succeed. “We ask women to embody the characteristics we often attribute to men in the workplace – aggression, boldness, forthrightness, risk-taking – as if these are the only characteristics that can contribute to professional success,” feminist writer Roxanne Gay wrote.

It’s not the first time Lagarde has spoken about the issue of women in positions of power. Two years ago in Japan she called on the country’s leaders to kickstart their weak economy by empowering women: “I urge everyone – all women and men of goodwill – to dare the difference and bet on women. I promise you this: you will not be disappointed.”